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Let's solve the problem step-by-step.

### 1. Finding the slope of the line
The line passes through the points \((-8, -6)\) and \((7, 4)\). The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the given points:
\[
m = \frac{4 - (-6)}{7 - (-8)} = \frac{4 + 6}{7 + 8} = \frac{10}{15} = \frac{2}{3}
\]

So, the slope \(m = \frac{2}{3}\).

### 2. Point-slope form of the equation
The point-slope form of the equation of a line is:

\[
y - y_1 = m(x - x_1)
\]

Substitute the slope \(m = \frac{2}{3}\) and one of the points, say \((-8, -6)\), into the equation:

\[
y - (-6) = \frac{2}{3}(x - (-8))
\]
\[
y + 6 = \frac{2}{3}(x + 8)
\]

### 3. Matching with the answer choices
This matches the third option in the provided answers:

\[
y + 6 = \frac{2}{3}(x + 8)
\]

Thus, the correct answer is **\(y + 6 = \frac{2}{3}(x + 8)\)**.

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Would you like any further details or explanations?

Here are 5 related questions to practice:
1. How would the equation change if the line passed through different points?
2. How do you convert from point-slope form to slope-intercept form?
3. What is the slope of a line parallel to this one?
4. What is the equation of a line perpendicular to the given line?
5. How do you find the y-intercept of a line from point-slope form?

**Tip:** Always check your slope calculation carefully, as it sets the foundation for the rest of the problem!

A line passes through the points (-8, -6) and (7, 4). What is an equation of the line in point-slope form?

Learn how to find the equation of a line passing through the points (-8, -6) and (7, 4) in point-slope form. This problem includes calculating the slope using the slope formula and applying it to the point-slope form of a line.

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